Change capacity constraints to be defined in the lowest resolution (#322

)

docs/src/how-to-use.md

@@ -158,7 +158,7 @@ The fields of `EnergyProblem` are
 
 * `graph`: The [Graph](@ref) object that defines the geometry of the energy problem.
 * `representative_periods`: A vector of [Representative Periods](@ref representative-periods).
-* `constraints_partitions`: A dictionary that connects pairs of asset and representative periods to [time partitions (vectors of time blocks)](@ref Partition)
+* `constraints_partitions`: Dictionaries that connects pairs of asset and representative periods to [time partitions (vectors of time blocks)](@ref Partition)
 * `model`: A JuMP model object. Initially `nothing`.
 * `solved`: A boolean indicating whether the `model` has been solved or not.
 * `objective_value`: After the model has been solved, this is the objective value at the solution.

docs/src/mathematical-formulation.md

@@ -1,7 +1,7 @@
 # [Mathematical Formulation](@id math-formulation)
 
-This section shows the mathematical formulation of the model.\
-The full mathematical formulation is also freely available in the [preprint](https://arxiv.org/abs/2309.07711).
+This section shows the mathematical formulation of the model assuming that the temporal definition of time steps is the same for all the elements in the model.\
+The full mathematical formulation considering variable temporal resolutions is also freely available in the [preprint](https://arxiv.org/abs/2309.07711).
 
 ## [Sets](@id math-sets)
 
@@ -85,7 +85,7 @@ flows\_variable\_cost &= \sum_{f \in \mathcal{F}} \sum_{rp \in \mathcal{RP}} \su
 
 ```math
 \begin{aligned}
-\sum_{f \in \mathcal{F}_{in}(a)} v^{flow}_{f,rp,k} - \sum_{f \in \mathcal{F}_{out}(a)} v^{flow}_{f,rp,k} \left\{\begin{array}{l} = \\ \geqslant \\ \leqslant \end{array}\right\} p^{profile}_{a,rp,k} \cdot p^{peak\_demand}_{a} \quad
+\sum_{f \in \mathcal{F}_{in}(a)} v^{flow}_{f,rp,k} - \sum_{f \in \mathcal{F}_{out}(a)} v^{flow}_{f,rp,k} = p^{profile}_{a,rp,k} \cdot p^{peak\_demand}_{a} \quad
 \\ \\ \forall a \in \mathcal{A}_c, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
 \end{aligned}
 ```
@@ -94,7 +94,7 @@ flows\_variable\_cost &= \sum_{f \in \mathcal{F}} \sum_{rp \in \mathcal{RP}} \su
 
 ```math
 \begin{aligned}
-s_{a,rp,k}^{level} = s_{a,rp,k-1}^{level} + p_{a,rp,k}^{inflow} + \cdot \sum_{f \in \mathcal{F}_{in}(a)} p^{eff}_f \cdot v^{flow}_{f,rp,k} - \sum_{f \in \mathcal{F}_{out}(a)} \frac{1}{p^{eff}_f} \cdot v^{flow}_{f,rp,k} \quad
+s_{a,rp,k}^{level} = s_{a,rp,k-1}^{level} + p_{a,rp,k}^{inflow} + \sum_{f \in \mathcal{F}_{in}(a)} p^{eff}_f \cdot v^{flow}_{f,rp,k} - \sum_{f \in \mathcal{F}_{out}(a)} \frac{1}{p^{eff}_f} \cdot v^{flow}_{f,rp,k} \quad
 \\ \\ \forall a \in \mathcal{A}_s, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
 \end{aligned}
 ```
@@ -117,9 +117,9 @@ s_{a,rp,k}^{level} = s_{a,rp,k-1}^{level} + p_{a,rp,k}^{inflow} + \cdot \sum_{f
 \end{aligned}
 ```
 
-### Constraints that Define Bounds of Flows Related to Energy Assets $\mathcal{A}$
+### Constraints that Define Capacity Limits of Flows Related to Energy Assets $\mathcal{A}$
 
-#### Contraint for the Overall Output Flows from an Asset
+#### Maximum Output Flows Limit
 
 ```math
 \begin{aligned}
@@ -128,7 +128,7 @@ s_{a,rp,k}^{level} = s_{a,rp,k-1}^{level} + p_{a,rp,k}^{inflow} + \cdot \sum_{f
 \end{aligned}
 ```
 
-#### Contraint for the Overall Input Flows from an Asset
+#### Maximum Input Flows Limit
 
 ```math
 \begin{aligned}
@@ -137,24 +137,15 @@ s_{a,rp,k}^{level} = s_{a,rp,k-1}^{level} + p_{a,rp,k}^{inflow} + \cdot \sum_{f
 \end{aligned}
 ```
 
-#### Upper Bound Constraint for Associated with Asset
-
-```math
-\begin{aligned}
-v^{flow}_{f,rp,k} \leq p^{profile}_{a,rp,k} \cdot \left(p^{init\_capacity}_{a} + p^{unit\_capacity}_a \cdot v^{investment}_a \right)  \quad \\ \\ \forall a \notin \mathcal{A}_h \cup \mathcal{A}_c,
-\forall f \in \mathcal{F}_{out}(a) \& \notin \mathcal{F}_t, \forall rp \in \mathcal{RP},\forall k \in \mathcal{K}
-\end{aligned}
-```
-
 #### Lower Bound Constraint Flows Associated with Asset
 
 ```math
 v^{flow}_{f,rp,k} \geq 0 \quad \forall f \notin \mathcal{F}_t, \forall rp \in \mathcal{RP}, \forall k \in \mathcal{k}
 ```
 
-### Constraints that Define Bounds for a Transport Flow $\mathcal{F}_t$
+### Constraints that Define Capacity Limits for a Transport Flow $\mathcal{F}_t$
 
-#### Upper Bound Constraint for Transport Flows
+#### Maximum Transport Flow Limit
 
 ```math
 \begin{aligned}
@@ -163,7 +154,7 @@ v^{flow}_{f,rp,k} \leq p^{profile}_{f,rp,k} \cdot \left(p^{init\_capacity}_{f} +
 \end{aligned}
 ```
 
-#### Lower Bound Constraint for Transport Flows
+#### Minimum Transport Flow Limit
 
 ```math
 \begin{aligned}
@@ -174,7 +165,7 @@ v^{flow}_{f,rp,k} \geq p^{profile}_{f,rp,k} \cdot \left(p^{init\_capacity}_{f} +
 
 ### Extra Constraints for Energy Storage Assets $\mathcal{A}_s$
 
-#### Upper and Lower Bound Constraints for Storage Level
+#### Maximum Storage Level Limit
 
 ```math
 0 \leq s_{a,rp,k}^{level} \leq p^{init\_storage\_capacity}_{a} + p^{ene\_to\_pow\_ratio}_a \cdot p^{unit\_capacity}_a \cdot v^{investment}_a \quad
@@ -190,14 +181,14 @@ s_{a,rp,k=K}^{level} \geq p^{init\_storage\_level}_{a} \quad
 
 ### Extra Constraints for Investments
 
-#### Upper Bound for $\mathcal{A}_i$
+#### Maximum Investment Limit for $\mathcal{A}_i$
 
 ```math
 v^{investment}_a \leq \frac{p^{investment\_limit}_a}{ p^{unit\_capacity}_a} \quad
 \\ \\ \forall a \in \mathcal{A}_i
 ```
 
-#### Upper Bound for $\mathcal{F}_i$
+#### Maximum Investment Limit for $\mathcal{F}_i$
 
 ```math
 v^{investment}_f \leq \frac{p^{investment\_limit}_f}{\max\{p^{export\_capacity}_f,p^{import\_capacity}_f\}} \quad

docs/src/tutorial.md

@@ -92,6 +92,8 @@ Creating an energy problem automatically computes this data, but since we are do
 constraints_partitions = compute_constraints_partitions(graph, representative_periods)
 ```
 
+The `constraints_partitions` has two dictionaries with the keys `:lowest_resolution` and `:highest_resolution`. The lowest resolution dictionary is mainly used to create the constraints for energy balance, whereas the highest resolution dictionary is mainly used to create the capacity constraints in the model.
+
 Now we can compute the model.
 
 ```@example manual
@@ -223,10 +225,13 @@ To create a vector with the all values of `storage_level` for a given `a` and `r
 ```@example solution
 a = first(labels(graph))
 rp = 1
-cons_parts = energy_problem.constraints_partitions
+cons_parts = energy_problem.constraints_partitions[:lowest_resolution]
 [solution.storage_level[a, rp, B] for B in cons_parts[(a, rp)]]
 ```
 
+> **Note**
+> Make sure to specify `constraints_partitions[:lowest_resolution]` since the storage level is determined in the energy balance constraint for the storage assets. This constraint is defined in the lowest resolution of all assets and flows involved.
+
 ### The solution inside the graph
 
 In addition to the solution object, the solution is also stored by the individual assets and flows when [`solve_model!`](@ref) is called - i.e., when using a [EnergyProblem](@ref) object.
@@ -252,20 +257,20 @@ To create a vector with the all values of `storage_level` for a given `a` and `r
 ```@example solution
 a = first(labels(graph))
 rp = 1
-cons_parts = energy_problem.constraints_partitions
+cons_parts = energy_problem.constraints_partitions[:lowest_resolution]
 [energy_problem.graph[a].storage_level[(rp, B)] for B in cons_parts[(a, rp)]]
 ```
 
 ### Values of constraints and expressions
 
 By accessing the model directly, we can query the values of constraints and expresions.
-For instance, we can get all incoming flow for a given asset at a given time block for a given representative periods with the following:
+For instance, we can get all incoming flow in the lowest resolution for a given asset at a given time block for a given representative periods with the following:
 
 ```@example solution
 using JuMP
 # a, rp, and cons_parts are defined above
 B = cons_parts[(a, rp)][1]
-value(energy_problem.model[:incoming_flow][a, rp, B])
+value(energy_problem.model[:incoming_flow_lowest_resolution][a, rp, B])
 ```
 
 The same can happen for constraints.